Arrays - Building Java Programs: A Back to Basics Approach - page 487

These percentages are almost exactly the numbers predicted by Benford's Law.
Data that obey Benford's Law have an interesting property. It doesn't matter what
scale you use for the data. So if you are measuring heights, for example, it doesn't mat-
ter whether you measure in feet, inches, meters, or furlongs. In our case, we counted the
number of people in each U.S. county. If we instead count the number of human hands
in each county, then we have to double each number. Look at the preceding table and see
if you can predict the result when you double each number. Here is the actual result:
Let's count those leading digits...
input file name? county2.txt
Digit Count Percent
1 900 28.67
2 555 17.68
3 415 13.22
4 322 10.26
5 242 7.71
6 209 6.66
7 190 6.05
8 173 5.51
9 133 4.24
Total 3139 100.00
Notice that there is very little change. Doubling the numbers has little effect because
if the original data is exponential in nature, then the same will be true of the doubled
numbers. Here is another sample run that triples the county population numbers:
Let's count those leading digits...
input file name? county3.txt
Digit Count Percent
1 926 29.50
2 549 17.49
3 385 12.27
4 327 10.42
5 258 8.22
6 228 7.26
7 193 6.15
8 143 4.56
9 130 4.14
Total 3139 100.00
Another data set that shows Benford characteristics is the count of sunspots that
occur on any given day. Robin McQuinn maintains a web page at http://sidc.oma.be/
html/sunspot.html that has daily counts of sunspots going back to 1818. Here is a
sample execution using these data: